Curricular Framework Mathematics-Algebra 1

Overview / Standards for Mathematical Content / Unit Focus / Standards for Mathematical Practice /
Unit 1
Modeling with Linear Equations and Inequalities /
  • N.Q.A.1
  • N.Q.A.2
  • N.Q.A.3
  • A.REI.B.3
  • A.REI.A.1
  • A.CED.A.4
  • A.SSE.A.1
  • A.CED.A.1
/
  • A.REI.A.1
  • A.CED.A.2
  • A.REI.D.10
  • S.ID.B.6
  • S.ID.C.7
  • S.ID.C.8
  • S.ID.C.9
  • A.REI.D.11
/ ·  Reason quantitatively and use units to solve problems
·  Solve [linear] equations and inequalities in one variable
·  Understand solving equations as a process of reasoning and explain the reasoning
·  Create equations that describe numbers or relationships
·  Interpret the structure of expressions
·  Represent and solve equations graphically
·  Summarize, represent, and interpret data on quantitative variables.
·  Interpret linear models / MP.1 Make sense of problems and persevere in solving them.
MP.2 Reason abstractly and quantitatively.
MP.3 Construct viable arguments & critique the reasoning of others.
MP.4 Model with mathematics.
MP.5 Use appropriate tools strategically.
MP.6 Attend to precision.
MP.7 Look for and make use of structure.
MP.8 Look for and express regularity in repeated reasoning.
Unit 1:
Suggested Open Educational Resources / N.Q.A.1 Runners' World
N.Q.A.2 Giving Raises
N.Q.A.3 Calories in a Sports Drink
A.REI.B.3, A.REI.A.1 Reasoning with linear inequalities
A.CED.A.4 Equations and Formulas / A.SSE.A.1 Kitchen Floor Tiles
A.CED.A.1 Planes and wheat
A-CED.A.1 Paying the rent
A.REI.A.1 Zero Product Property 1
A.CED.A.2 Clea on an Escalator
S.ID.B.6,S.ID.C.7-9 Coffee and Crime
Unit 2
Modeling with Linear Functions, Linear Systems, & Exponential Functions /
  • A.REI.C.6
  • A.CED.A.3
  • A.REI.C.5
  • A.REI.D.12
  • F.IF.A.1
  • F.IF.A.2
  • F.LE.A.1
  • F.LE.A.2
  • F.IF.A.3
/
  • F.BF.A.1
  • A.SSE.A.1
  • A.SSE.B.3
  • F.IF.B.4
  • F.LE.B.5
  • F.IF.B.5
  • F.IF.B.6
  • F.IF.C.9
  • F.IF.C.7
/ ·  Solve linear systems of equations
·  Create equations that describe numbers or relationships
·  Interpret the structure of expressions
·  Represent and solve equations and inequalities graphically
·  Construct & compare linear & exponential models
·  Interpret expressions for functions in terms of the situation
·  Build a function that models a relationship between two quantities
·  Understand the concept of a function and use function notation
·  Interpret functions that arise in applications in terms of the context
·  Analyze functions using different representations
Unit 2:
Suggested Open Educational Resources / A.REI.C.6 Cash Box
A.CED.A.3 Dimes and Quarters
A.REI.C.5 Solving Two Equations in Two Unknowns
A.REI.D.12 Fishing Adventures 3
F.IF.A.1 The Parking Lot
F.IF.A.2 Yam in the Oven
F.LE.A.1 Finding Linear and Exponential Models
F.LE.A.2 Interesting Interest Rates / F.BF.A.1a Skeleton Tower
A.SSE.A.1 Mixing Candies
F.IF.B.4 Warming and Cooling
F.IF.B.4, F.IF.B.5 Average Cost
F.LE.B.5 US Population 1982-1988
F.IF.B.6 Temperature Change
F.IF.C.7b Bank Account Balance
Unit 3
Quadratic Equations, Functions & Polynomials /
  • A.APR.A.1
  • A.SSE.A.2
  • A.REI.B.4
  • A.CED.A.1
  • F.IF.B.4*
  • F.IF.B.5*
  • A.SSE.B.3
  • F.BF.A.1
/
  • F.IF.C.7*
  • F.IF.C.8*
  • F.IF.C.9*
  • F.IF.B.6
  • F.LE.A.3
  • F.BF.B.3
  • A.REI.D.11
  • A.APR.B.3
  • N.RN.B.3
/ ·  Perform arithmetic operations on polynomials
·  Understand the relationship between zeros and factors
·  Interpret the structure of expressions
·  Solve equations and inequalities in one variable
·  Create equations that describe numbers or relationships
·  Interpret functions that arise in applications in terms of the context
·  Represent and solve equations and inequalities graphically
·  Build a function that models a relationship between two quantities
·  Construct & compare linear, quadratic, & exponential models
·  Build new functions from existing functions
·  Analyze functions using different representations
·  Use properties of rational and irrational numbers / MP.1 Make sense of problems and persevere in solving them.
MP.2 Reason abstractly and quantitatively.
MP.3 Construct viable arguments & critique the reasoning of others.
MP.4 Model with mathematics.
MP.5 Use appropriate tools strategically.
MP.6 Attend to precision.
MP.7 Look for and make use of structure.
MP.8 Look for and express regularity in repeated reasoning.
Unit 3:
Suggested Open Educational Resources / A.APR.A.1 Powers of 11
A.SSE.A.2 Equivalent Expressions
A.REI.B.4 Visualizing Completing the Square
A.REI.B.4 Braking Distance
A.REI.B.4 Two Squares are Equal
F.IF.B.4 Words – Tables - Graphs
F.IF.B.5 The restaurant
A.SSE.B.3 Profit of a company
A.SSE.B.3 Rewriting a Quadratic Expression
F.IF.C.7a Graphs of Quadratic Functions / F.IF.C.8a Springboard Dive
F.IF.C.8a Which Function?
F.IF.B.9 Throwing Baseballs
F.IF.B.6 Mathemafish Population
F.LE.A.3 Population and Food Supply
F.BF.B.3 Identifying Even and Odd Functions
F.BF.B.3 Transforming the graph of a function
A.REI.D.11 Introduction to Polynomials – College Fund
A.APR.B.3 Graphing from Factors 1
N.RN.B.3 Operations with Rational and Irrational Numbers
Unit 4
Modeling with Statistics /
  • S.ID.A.1
  • S.ID.A.2
  • S.ID.A.3
  • S.ID.B.5
  • S.ID.B.6
/
  • F.IF.B.4*
  • F.IF.B.5*
/ ·  Summarize, represent, and interpret data on a single count or measurement variable
·  Summarize, represent, and interpret data on two categorical and quantitative variables
·  Interpret functions that arise in applications in terms of the context
Unit 4:
Suggested Open Educational Resources / S.ID.A.1-3 Haircut Costs
S.ID.A.1-3 Speed Trap
S.ID.A.2-3 Measuring Variability in a Data Set
S.ID.A.3 Identifying Outliers
S.ID.B.5 Support for a Longer School Day?
S.ID.B.6 Laptop Battery Charge 2
F.IF.B.4 The Aquarium
F.IF.B.4 Containers
F.IF.B.4-5 The Canoe Trip, Variation 2
Unit 1 Algebra 1
Content & Practice Standards / Suggested Standards for Mathematical Practice / Critical Knowledge & Skills
  • N.Q.A.1. Use units as a way to understand problems and to guide the solution of multi-step problems; Choose and interpret units consistently in formulas; Choose and interpret the scale and the origin in graphs and data displays.
  • N.Q.A.2. Define appropriate quantities for the purpose of descriptive modeling.
  • N.Q.A.3. Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
/ MP.1 Make sense of problems and persevere in solving them.
MP 2 Reason abstractly and quantitatively.
MP.4 Model with mathematics.
MP.5 Use appropriate tools strategically. / Concept(s):
·  Units are associated with variables in expressions and equations in context.
·  Quantities may be used to model attributes of real world situations.
·  Measurement tools have an inherent amount of uncertainty in measurement.
Students are able to:
·  use units to understand real world problems.
·  use units to guide the solution of multi-step real world problems (e.g. dimensional analysis).
·  choose and interpret units while using formulas to solve problems.
·  identify and define appropriate quantities for descriptive modeling.
·  choose a level of accuracy when reporting measurement quantities.
Learning Goal 1: Solve multi-step problems, using units to guide the solution, interpreting units consistently in formulas and choosing an appropriate level of accuracy on measurement quantities. Develop descriptive models by defining appropriate quantities.
  • A.REI.B.3. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
  • A.REI.A.1. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
  • A.CED.A.4. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm's law V = IR to highlight resistance R.
/ MP 2 Reason abstractly and quantitatively.
MP.6 Attend to precision.
MP.7 Look for and make use of structure. / Concept(s).
·  Literal equations can be rearranged using the properties of equality.
Students are able to.
·  solve linear equations with coefficients represented by letters in one variable.
·  use the properties of equality to justify steps in solving linear equations.
·  solve linear inequalities in one variable.
·  rearrange linear formulas and literal equations, isolating a specific variable.
Learning Goal 2. Solve linear equations and inequalities in one variable (including literal equations); justify each step in the process.
  • A.SSE.A.1. Interpret expressions that represent a quantity in terms of its context.
A.SSE.A.1a. Interpret parts of an expression, such as terms, factors, and coefficients. / MP.1 Make sense of problems and persevere in solving them.
MP 2 Reason abstractly and quantitatively. / Concept(s): No new concept(s) introduced
Students are able to:
·  identify different parts of an expression, including terms, factors and constants.
·  explain the meaning of parts of an expression in context.
Learning Goal 3: Interpret terms, factors, coefficients, and other parts of expressions in terms of a context .
  • A.CED.A.1. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear functions and quadratic functions, and simple rational and exponential functions.
  • A.REI.A.1. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
/ MP 2 Reason abstractly and quantitatively.
MP.4 Model with mathematics.
MP.7 Look for and make use of structure. / Concept(s):
·  Equations and inequalities describe relationships.
·  Equations can represent real-world and mathematical problems.
Students are able to:
·  identify and describe relationships between quantities in word problems.
·  create linear equations in one variable.
·  create linear inequalities in one variable.
·  use equations and inequalities to solve real world problems.
·  explain each step in the solution process.
Learning Goal 4: Create linear equations and inequalities in one variable and use them in contextual situations to solve problems. Justify each step in the process and the solution.
  • A.CED.A.2. Create equations in two or more variables to represent relationships between quantities; Graph equations on coordinate axes with labels and scales.
  • N.Q.A.1. Use units as a way to understand problems and to guide the solution of multi-step problems; Choose and interpret units consistently in formulas; Choose and interpret the scale and the origin in graphs and data displays.
  • A.REI.D.10. Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). [Focus on linear equations.]
/ MP 2 Reason abstractly and quantitatively.
MP.4 Model with mathematics.
MP.7 Look for and make use of structure. / Concept(s):
·  Equations represent quantitative relationships.
Students are able to:
·  create linear equations in two variables, including those from a context.
·  select appropriate scales for constructing a graph.
·  interpret the origin in graphs.
·  graph equations on coordinate axes, including labels and scales.
·  identify and describe the solutions in the graph of an equation.
Learning Goal 5: Create linear equations in two variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
  • S.ID.B.6. Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
S.ID.B.6a. Fit a function to the data (including the use of technology); use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.
S.ID.B.6c. Fit a linear function for a scatter plot that suggests a linear association.
  • S.ID.C.7. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
  • S.ID.C.8. Compute (using technology) and interpret the correlation coefficient of a linear fit.
  • S.ID.C.9. Distinguish between correlation and causation.
/ MP.1 Make sense of problems and persevere in solving them.
MP 2 Reason abstractly and quantitatively.
MP.4 Model with mathematics.
MP.5 Use appropriate tools strategically.
MP.6 Attend to precision. / Concept(s):
·  Scatter plots represent the relationship between two variables.
·  Scatter plots can be used to determine the nature of the association between the variables.
·  Linear models may be developed by fitting a linear function to approximately linear data.
·  The correlation coefficient represents the strength of a linear association.
Students are able to:
·  distinguish linear models representing approximately linear data from linear. equations representing “perfectly” linear relationships.
·  create a scatter plot and sketch a line of best fit.
·  fit a linear function to data using technology.
·  solve problems using prediction equations.
·  interpret the slope and the intercepts of the linear model in context.
·  determine the correlation coefficient for the linear model using technology.
·  determine the direction and strength of the linear association between two variables.
Learning Goal 6: Represent data on a scatter plot, describe how the variables are related and use technology to fit a function to data.
Learning Goal 7: Interpret the slope, intercept, and correlation coefficient of a data set of a linear model; distinguish between correlation and causation.
  • A.REI.D.11. Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.* [Focus on linear equations.]
/ MP.1 Make sense of problems and persevere in solving them.
MP.3 Construct viable arguments and critique the reasoning of others.
MP.5 Use appropriate tools strategically. / Concept(s):
·  y = f(x), y=g(x) represent a system of equations.
·  Systems of equations can be solved graphically (8.EE.C.8).
Students are able to:
·  explain the relationship between the x-coordinate of a point of intersection and the solution to the equation f(x) = g(x) for linear equations y = f(x) and y = g(x).
·  find approximate solutions to the system by making a table of values, graphing, and finding successive approximations.
Learning Goal 8: Explain why the solutions of the equation f(x) = g(x) are the x-coordinates of the points where the graphs of the linear equations y=f(x) and y=g(x) intersect. ** function notation is not introduced here
Learning Goal 9: Find approximate solutions of f(x) = g(x), where f(x) and g(x) are linear functions, by making a table of values, using technology to graph and finding successive approximations.
Unit 1 Algebra 1 What This May Look Like
District/School Formative Assessment Plan / District/School Summative Assessment Plan
Formative assessment informs instruction and is ongoing throughout a unit to determine how students are progressing against the standards. / Summative assessment is an opportunity for students to demonstrate mastery of the skills taught during a particular unit.